The random variables X and Y are N(0,2) (Normal or Gaussian distributed) and independent. Find the PDF and CDF of Z = 2X + 3Y.
Two fair dice are rolled. Find the joint probability mass function of X and Y when X is the largest value obtained on any die and Y is the sum of the values.
Given the joint PMF of X and Y as Px,y(x,y)= {1/4 (x,y)=(1,1) } {1/4 (x,y)=(1,1) } {1/2 (x,y)=(0,0) } { 0 otherwise } (a) Find E[X], E[Y], and E[XY], (b) Show that X and Y are uncorrelated, (c) Determine if X and Y are independent or not.
The joint density function of X and Y is Fx,y(x,y)= { x+y 0<x<1.0<y<1 0 otherwise }
a) Are X and Y independent? b) Find the density function of X? c) Find P(X+Y < 1)=?
Suppose the joint density function of X and Y is given by
Fx,y(x,y)= {((e^x/y) * (e^y))/y 0<x<oo , 0<y<oo 0 otherwise }
a) Find the conditional density of x, given that Y=y. b) Find P(X > 1  Y = y).
